Question

question 1 pts
the graph of which equation is parallel to the graph of 2x - y = -1?
a 2x + y = 8
b ( y = -\frac{1}{2}x + 3 )
c ( y - 1 = 2(x - 3) )
d ( y = -2x - 1 )

question 1 pts
cassidy’s family is driving home from vacation at an average speed of 55 mph. after 2 hours 110 miles from home. what is an equation, in point - slope form, that represents their distance y, after x hours?
a. ( y - 110 = -55(x - 2) )
b. ( y - 55 = 110(x - 2) )
c. ( y - 2 = 55(x - 110) )
d. ( y + 110 = -55(x + 2) )

Explanation:

First Question (Parallel Equations)

Step1: Find slope of given line

Rewrite \(2x - y = -1\) in slope - intercept form (\(y=mx + b\), where \(m\) is slope).
\(y=2x + 1\), so slope \(m = 2\).

Step2: Find slopes of options

• Option A: \(2x + y=8\Rightarrow y=-2x + 8\), slope \(=-2\).
• Option B: \(y =-\frac{1}{2}x+3\), slope \(=-\frac{1}{2}\).
• Option C: \(y - 1=2(x - 3)\Rightarrow y=2x-5\), slope \(=2\).
• Option D: \(y=-2x - 1\), slope \(=-2\).

Step1: Identify slope and point

• Speed is \(55\) mph, but since they are driving home, the distance \(y\) decreases as \(x\) (time) increases. So slope \(m=-55\).
• After \(x = 2\) hours, distance \(y = 110\) miles. So the point is \((2,110)\).

Step2: Apply point - slope formula

Point - slope formula: \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(2,110)\) and \(m=-55\).
Substitute: \(y - 110=-55(x - 2)\).

Answer:

C. \(y - 1 = 2(x - 3)\)

Second Question (Point - Slope Form)